Constrained Portfolio Optimization via Quantum Approximate Optimization Algorithm (QAOA) with XY-Mixers and Trotterized Initialization: A Hybrid Approach for Direct Indexing

Battle Count: 73

Highly relevant to quantitative trading and asset management. The paper directly addresses cardinality-constrained portfolio selection, a core problem in Direct Indexing, SMA construction, and institutional portfolio management. The QAOA-XY approach demonstrates superior Sharpe Ratio (1.81 vs 1.31 for SA) in a walk-forward backtest. However, practical deployment is limited by the small universe size (N=10), high turnover, and reliance on simulation rather than real quantum hardware. The methodology is more immediately applicable as a quantum-inspired optimization framework than as a deployable trading system. The turnover trade-off discussion is particularly relevant for practitioners managing transaction costs.

High complexity due to multiple interacting components: (1) Dicke state preparation for arbitrary N and K, (2) XY-mixer Hamiltonian construction on complete graphs, (3) Trotterized parameter initialization schedules, (4) variational quantum circuit optimization with Adam optimizer and early stopping, (5) probability vector readout with Hamming-weight filtering, (6) classical rescored candidate selection, (7) SLSQP continuous weight allocation with box constraints, (8) Simulated Annealing QUBO encoding as baseline, (9) HRP fallback, (10) walk-forward backtesting with transaction cost modeling. Requires expertise in quantum computing (PennyLane), portfolio theory, and numerical optimization. The statevector simulation limits scalability beyond ~20 qubits.

The paper provides detailed hyperparameters (Table I), explicit algorithm pseudocode (Algorithm 1), specific library references (PennyLane, PyPortfolioOpt, yfinance, neal), and full experimental configuration. Data source (Yahoo Finance via yfinance) is publicly accessible. However, no GitHub repository or code link is provided. The Dicke state preparation and XY-mixer implementation details are described mathematically but not as executable code. The 2025 backtest period is in the future relative to typical training data, which may affect exact reproducibility of price data.